Fermionic Vector, Matrix and Tensor Models

Fermionic Majorana Quantum Mechanics play crucial role in the modern high-energy physics due the recent discovery of the SYK model and its connection to the AdS/CFT correspondence. I will review the fermonic tensor models and its reduction to the matrix and vector models. The tensor models are proposed to have the same dynamics as the SYK model but does not contain disorder that makes it very compelling for the high-energy physics application. In the cases of matrix and vector models we show that the system is integrable and we can compute the spectrum of the model by the virtue of the representation theory. For vector models we additionally show that the system has a maximal temperature - that’s quite peculiar for the one-dimensional models. At the end, I will propose a method that allows to study the gauged version of such models on an experiment or in quantum computers.